622: the number, its properties, and the year AD 622

Overview of 622 as an integer (factorization, representations, classifications) and as a historical year, notably the Hijra that marks the start of the Islamic calendar.

622 is an integer that can be treated both as a mathematical object and as a calendar year. As a number it lies between 621 and 623 and has simple arithmetic structure; as a year, 622 CE is best known for the migration of Muhammad from Mecca to Yathrib (the Hijra), an event that serves as the epoch for the Islamic lunar calendar.

Mathematical properties

In arithmetic terms 622 is even and composite. Its prime factorization is 2 × 311, so it is a semiprime (the product of two primes). Important basic invariants include:

Divisors: 1, 2, 311, 622.
Euler's totient: φ(622) = 310.
Sum of proper divisors: 1 + 2 + 311 = 314, so 622 is a deficient number (the proper divisors sum to less than the number).
Numeral representations: Roman = DCXXII; binary = 1001101110; octal = 1156; hexadecimal = 0x26E.

Historical year (AD 622)

Year 622 CE is a turning point in religious and political history because of the Hijra, Muhammad's migration from Mecca to the city later known as Medina. That migration established the first Muslim community governed by Islamic principles and is conventionally taken as year 1 in the Hijri calendar. The event altered the social and political landscape of the Arabian Peninsula and provided the foundation for the later expansion of Islam.

Other contexts and notable facts

Numbers like 622 appear in many mundane contexts—catalog numbers, model names, and route designations—but such uses are arbitrary and vary by country and system. Mathematically, 622's simplicity (one small prime factor 2 and one larger prime 311) makes it easy to work with in elementary number theory examples: it is a simple example of an even semiprime and illustrates concepts such as divisor sums and Euler's totient.

In summary, 622 is notable both as a straightforward composite integer with clean, verifiable properties and as the calendar year associated with a major historical turning point. When encountered in texts, context will usually make clear whether the reference is numerical, calendrical, or mundane (e.g., a model number).